Some Estimates of Schrödinger-Type Operators with Certain Nonnegative Potentials
We consider the Schrödinger-type operator H=(−Δ)2+V2, where the nonnegative potential V belongs to the reverse Hölder class Bq1 for q1≥n/2, n≥5. The Lp estimates of the operator ∇4H−1 related to H are obtained when V∈Bq1 and 1<p≤q1/2. We also obtain the weak-type estimates of the operator ∇4H−1...
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| Format: | Article |
| Language: | English |
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Wiley
2008-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2008/214030 |
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| _version_ | 1850211764559413248 |
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| author | Yu Liu Youzheng Ding |
| author_facet | Yu Liu Youzheng Ding |
| author_sort | Yu Liu |
| collection | DOAJ |
| description | We consider the Schrödinger-type operator H=(−Δ)2+V2, where the nonnegative potential V belongs to the reverse Hölder class Bq1 for q1≥n/2, n≥5. The Lp estimates of the operator ∇4H−1 related to H are obtained when V∈Bq1 and 1<p≤q1/2. We also obtain the weak-type estimates of the operator ∇4H−1 under the same condition of V. |
| format | Article |
| id | doaj-art-8fcaaa6403cf493285bc939f84dc74dd |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2008-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-8fcaaa6403cf493285bc939f84dc74dd2025-08-20T02:09:29ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252008-01-01200810.1155/2008/214030214030Some Estimates of Schrödinger-Type Operators with Certain Nonnegative PotentialsYu Liu0Youzheng Ding1Department of Mathematics and Mechanics, University of Science and Technology Beijing, Beijing 100083, ChinaCollege of Science, Shandong Jianzhu University, Jinan 250101, Shandong Province, ChinaWe consider the Schrödinger-type operator H=(−Δ)2+V2, where the nonnegative potential V belongs to the reverse Hölder class Bq1 for q1≥n/2, n≥5. The Lp estimates of the operator ∇4H−1 related to H are obtained when V∈Bq1 and 1<p≤q1/2. We also obtain the weak-type estimates of the operator ∇4H−1 under the same condition of V.http://dx.doi.org/10.1155/2008/214030 |
| spellingShingle | Yu Liu Youzheng Ding Some Estimates of Schrödinger-Type Operators with Certain Nonnegative Potentials International Journal of Mathematics and Mathematical Sciences |
| title | Some Estimates of Schrödinger-Type Operators with Certain Nonnegative Potentials |
| title_full | Some Estimates of Schrödinger-Type Operators with Certain Nonnegative Potentials |
| title_fullStr | Some Estimates of Schrödinger-Type Operators with Certain Nonnegative Potentials |
| title_full_unstemmed | Some Estimates of Schrödinger-Type Operators with Certain Nonnegative Potentials |
| title_short | Some Estimates of Schrödinger-Type Operators with Certain Nonnegative Potentials |
| title_sort | some estimates of schrodinger type operators with certain nonnegative potentials |
| url | http://dx.doi.org/10.1155/2008/214030 |
| work_keys_str_mv | AT yuliu someestimatesofschrodingertypeoperatorswithcertainnonnegativepotentials AT youzhengding someestimatesofschrodingertypeoperatorswithcertainnonnegativepotentials |